2 research outputs found
Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices
It has been shown in earlier works that for Q=0 and L a multiple of N, the
ground state sector eigenspace of the superintegrable tau_2(t_q) model is
highly degenerate and is generated by a quantum loop algebra L(sl_2).
Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2
algebras. For Q not equal 0, we shall show here that the corresponding
eigenspace of tau_2(t_q) is still highly degenerate, but splits into two
spaces, each containing 2^{r-1} independent eigenvectors. The generators for
the sl_2 subalgebras, and also for the quantum loop subalgebra, are given
generalizing those in the Q=0 case. However, the Serre relations for the
generators of the loop subalgebra are only proven for some states, tested on
small systems and conjectured otherwise. Assuming their validity we construct
the eigenvectors of the Q not equal 0 ground state sectors for the transfer
matrix of the superintegrable chiral Potts model.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 28 pages,
uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added,
improvements and minor corrections made, erratum to paper 2 included. Version
3: Small paragraph added in introductio
Including a phase in the Bethe equations of the Hubbard model
We compute the Bethe equations of generalized Hubbard models, and study their
thermodynamical limit. We argue how they can be connected to the ones found in
the context of AdS/CFT correspondence, in particular with the so-called
dressing phase problem. We also show how the models can be interpreted, in
condensed matter physics, as integrable multi-leg Hubbard models.Comment: 30 page